Welcome Accelerated Algebra 2! Tear-Out: Pg. 487-492 (Class notes) Updates: U8Q1 will be 4/24 Unit Circle Quiz will be 4/24 U8T will be 5/1
Agenda (1) Warm-Up (2) Review U8H1 (3) Finish Trig Review (4) Standard Angle Positions (32-1) (5) Closure
Warm-Up Find the value of x and round to the nearest tenth.
Review U8H1 U8H1: Worksheet 13.1 #2-8
Review of Trigonometry From Geometry you studied special right triangles; 30-60-90 and 45-45-90. When working with trigonometric functions you will commonly refer to the special right triangles such that you do not have to use a calculator. I will show you the derivation of each on the board. Copy into your notebook!
Review of Trigonometry q Derive 45-45-90 Triangle Relationship. o Think What shape can you split into two 45-45-90 triangles? o Lets ^ind sine, cosine, and tangent of the acute angle. q Derive 30-60-90 Triangle Relationship. o Think What shape can you split into two 30-60-90 triangles? o Lets ^ind sine, cosine, and tangent of the acute angles.
Review of Trigonometry
Review of Trigonometry We have more Trigonometric Functions J
Review of Trigonometry
Review of Trigonometry
I will leave one page blank for supplemental notes. Today s Lesson #: 32-1 Topic: Standard Angle Positions LO#2: Draw angles in standard position and determine coterminal and reference angles.
Pg. 487 We will read the ^irst paragraph together.
Standard Position o The vertex of an angle is at the origin and one ray is on the positive x-axis. Ø Initial side of the angle is the ray on the positive x- axis. Ø Terminal side is the other ray of the angle. Counter- Clockwise! Clockwise!
Pg. 487 In the MY NOTES column draw an angle in standard position with a measure of 298. In the MY NOTES column draw an angle in standard position with a measure of -298.
Pg. 488 Do TRY THESE A (a-b). (1.5 mins) Ø What angle, between 0 and -360 has the same terminal side as (b)? Discuss with your vertical partner. Ø What angle, between 0 and 360 has the same terminal side as (b)? Discuss with your horizontal partner.
Pg. 488 Ø What angle, between 0 and -360 has the same terminal side as 405? Discuss with your vertical partner. Ø What angle, between 0 and 360 has the same terminal side as 405? Discuss with your horizontal partner.
Pg. 488 Answer #1 independently in one complete sentence. (30 secs)
Pg. 489 Do TRY THESE D (a-c) independently. (1.5 mins) Compare with your diagonal partner.
Pg. 489 Independently answer #4 and #6. (2 mins)
Coterminal Angles o Angles in standard position with the same terminal side. o To ^ind coterminal angles add or subtract multiples of 360. o Note there are an in^inite number of coterminal angles.
Pg. 490 We eventually will need to connect these angles in standard position to right triangles such that we can use trigonometry. We will need to understand reference angles.
Pg. 490 In the MY NOTES COLUMN draw an angle in standard position with the measure of 250. As a class we will ^ind the reference angle. In the MY NOTES COLUMN draw an angle in standard position with the measure of 357. In the MY NOTES COLUMN draw an angle in standard position with the measure of 162. In the MY NOTES COLUMN draw an angle in standard position with the measure of 25.
Pg. 491 Do TRY THESE E (a, c, f). (2 mins)
Reference Angle o The positive acute angle formed by the terminal side of θ and the x-axis.
Pg. 492 Reference angles allow us to ^ind the six trigonometric functions for a given θ. In the MY NOTES COLUMN ^ind the reference angle for an angle in standard position with a measure of 1845. Find the six trigonometric function using the reference angle. You can check your ratios using your calculator.
Pg. 492 In the MY NOTES COLUMN ^ind the reference angle for an angle in standard position with a measure of -480. Find the six trigonometric function using the reference angle (be careful with your signs).
Closure You will get a Closure template and this template will help me see daily if you are understanding the lessons. Put your name on the template. Choose one of the boxes to complete. I will give you about 5-8 minutes in class to Ainish and then you will turn it in to your periods tray. I will stamp to signal that your closure is complete but I may or may not be able to read each one. At the end of the unit I will grade 2-3 of your closures. I will grade random ones!